Analytical and numerical study of validation test-cases for multi-physic problems: application to magneto-hydro-dynamic

18p.International audienceThe present paper is concerned with the numerical simulation of Magneto-Hydro-Dynamic (MHD) problems with industrial tools. MHD has received attention some twenty to thirty years ago as a possible alternative in propulsion applications; MHD propelled ships have even been designed for that purpose. However, such propulsion systems have been proved of low efficiency and fundamental researches in the area have progressively received much less attention over the past decades. Numerical simulation of MHD problem could however provide interesting solutions in the field of turbulent flow control. The development of recent efficient numerical techniques for multi-physic applications provide promising tool for the engineer for that purpose. In the present paper, some elementary test cases in laminar flow with magnetic forcing terms are analysed; equations of the coupled problem are exposed, analytical solutions are derived in each case and are compared to numerical solutions obtained with a numerical tool for multi-physic applications. The present work can be seen as a validation of numerical tools (based on the finite element method) for academic as well as industrial application purposes